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DOI : 10.1080/03461230701766882

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Scandinavian Actuarial Journal 2008, 1 (2008) 41-60

On Finite-Time Ruin Probabilities for Classical Risk Models

Claude Lefèvre (  Auteur correspondant ) 1, Stéphane Loisel 2

(01/2008)

This paper is concerned with the problem of ruin in the classical compound binomial and compound Poisson risk models. Our primary purpose is to extend to those models an exact formula derived by Picard and Lefèvre (1997) for the probability of (non-)ruin within finite time. First, a standard method based on the ballot theorem and an argument of Seal-type provides an initial (known) formula for that probability. Then, a concept of pseudo-distributions for the cumulated claim amounts, combined with some simple implications of the ballot theorem, leads to the desired formula. Two expressions for the (non-)ruin probability over an infinite horizon are also deduced as corollaries. Finally, an illustration within the framework of Solvency II is briefly presented.

1 :	Département de Mathématique
	Université Libre de Bruxelles
2 :	Laboratoire de Sciences Actuarielle et Financière (SAF)
	Université Claude Bernard - Lyon I : EA2429

Équipe de recherche : Cahiers de Recherche de l'ISFA

Domaine

:

Sciences de l'Homme et Société/Economies et finances Mathématiques/Probabilités

Mots Clés : ruin probability – finite and infinite horizon – compound binomial model – compound Poisson model – ballot theorem – pseudo-distributions – Solvency II – Value-at-Risk.

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Contributeur : Stéphane Loisel <>

Soumis le : Vendredi 31 Août 2007, 00:34:42

Dernière modification le : Mercredi 1 Avril 2009, 14:33:57